f4 {NPHMC}

Function Four

Description

The fourth integrate function

Usage

f4(t, accrualtime, followuptime, accrualdist, beta0, gamma0, pi0, survdist,
 k, lambda0)

Arguments

t

time variable

accrualtime

length of accrual period.

followuptime

length of follow-up time.

accrualdist

accrual pattern. It can be "uniform", "increasing" or "decreasing".

beta0

log hazard ratio of uncured patients

gamma0

log odds ratio of cure rates between the two arms

pi0

cure rate for the control arm, which is between 0 and 1.

survdist

survival distribution of uncured patients. It can be "exp" or "weib".

k

if survdist = "weib", the shape parameter k needs to be specified. By default k = 1, which refers to the exponential distribution.

lambda0

the scale parameter of exponential distribution or Weibull distribution for survival times of uncured patients in the control arm.

The density function of Weibull distribution with shape parameter k and scale parameter \lambda_0 is given by

f(t)=\lambda_{0}k(\lambda_{0}t)^{k-1}\exp(-(\lambda_{0}t)^k),

for t > 0, and the corresponding survival distribution is

S(t)=\exp(-(\lambda_0 t)^k).